The generation of strong and pure magnetic fields is of great interest in many technical applications. In particular, it is very important for clinical magnetic resonance imaging (MRI). A major specification of the static field in MRI is that it has to be substantially homogeneous over a predetermined region, known in the art as the "diameter spherical imaging volume" or "dsv." Errors less than 20 parts per million peak-to-peak (or 10 parts per million rms) over a dsv having a diameter of 45-50 cm are often required. Conventional medical MRI systems are typically around 1.6-2.0 m in length with free bore diameters in the range of 0.8-1.0 m. Normally, the magnet is symmetric and the midpoint of the dsv is located at the geometric center of the magnet's structure. The central uniformity of symmetrical fields is often analyzed by a zonal spherical harmonic expansion.
The basic components of a magnet system 10 useful for performing magnetic resonance investigations are shown in FIG. 14. The system of this figure is suitable for producing diagnostic images for human studies, similar systems being used for other applications.
System 10 includes magnet housing 12, superconducting magnet 13, shim coils 14, gradient coils 16, RF coils 18, and patient table 20. As is well known in the art, magnet 13 serves to produce a substantially uniform field (the B.sub.0 field) in the dsv. Discussions of MRI, including magnet systems for use in conducting MRI studies, can be found in, for example, Mansfield et al., NMR in Imaging and Biomedicine, Academic Press, Orlando, Fla., 1982. See also McDougall, U.S. Pat. No. 4,689,591; McDougall et al., U.S. Pat. No. 4,701,736; Dorri et al., U.S. Pat. No. 5,416,415; Dorri et al., U.S. Pat. No. 5,428,292; and Chari et al., International Publication No. WO 94/06034.
In modern medical imaging, there is a distinct and long-felt need for magnet systems which have a shorter overall length. The typical patient aperture of a conventional MRI machine is a cylindrical space having a diameter of about 0.6-0.8 meters, i.e., just large enough to accept the patient's shoulders, and a length of about 2.0 meters or more. The patient's head and upper torso are normally located near the center of the patient aperture, which means that they are typically about a meter from the end of the magnet system.
Not surprisingly, many patients suffer from claustrophobia when placed in such a space. Also, the distance of the patient's head and torso from the end of the magnet system means that physicians cannot easily assist or personally monitor the patient during an MRI procedure, which can last as long as an hour or two.
In addition to its affects on the patient, the length of the magnet is a primary factor in determining the cost of an MRI machine, as well as the costs involved in the siting of such a machine. In order to be safely used, MRI machines often need to be shielded so that the magnetic fields surrounding the machine at the location of the operator are below FDA-specified exposure levels. By means of shielding, the operator can be safely sited much closer to the magnet than in an unshielded system. Longer magnets require more internal shielding and larger shielded rooms for such safe usage, thus leading to higher costs.
In recent years, there has been an increasing interest in the optimal design of clinical MRI magnets. See, for example, M. W. Garrett, "Axially symmetric systems for generating and measuring magnetic fields. Part I," J. Appl. Phys. 22, 1091-1107 (1951); M. W. Garrett, "Thick cylindrical coil systems for strong magnetic fields with field or gradient homogeneities of the 6.sup.th to 20.sup.th order," J. Appl. Phys. 38, 2563-2586 (1967); H. Siebold, "Design optimization of main, gradient and RF field coils for MR imaging," IEEE Trans. Magn. 26, 841-846 (1990); F. J. Davies, R. T. Elliott, and D. G. Hawkesworth, "A 2-Tesla active shield magnet for whole body imaging and spectroscopy," IEEE Trans. Magn. 27, 1677-1680 (1991); A. K. Kalafala, "Optimized configurations for actively shielded magnetic resonance imaging magnets," IEEE Trans. Magn. 27, 1696-1699 (1991); and W. M. Schmidt, R. R. Huson, W. W. Mackay, and R. M. Rocha, "A 4 Tesla/1 meter superferric MRI magnet," IEEE Trans. Magn. 27, 1681-1684 (1991).
In addition to the above work, Pissanetzky has proposed an approach to field design based on a hybridized methodology incorporating ideas from finite elements, analytical techniques, and other numerical methods. See S. Pissanetzky, "Structured coil for NMR applications," IEEE Trans. Magn., 28, 1961-1968 (1992). Thompson has illustrated a method based on a variational approach with constraints introduced by Lagrange multipliers. The analytical aspects of the variational calculus were combined with numerical techniques to obtain optimal spatial coil distributions. See Michael R. Thompson, Robert W. Brown, and Vishnu C. Srivastava, "An inverse approach to design of MRI main magnets", IEEE Trans. Magn., 30, 108-112, (1994); and Robert W. Brown, Hiroyukai Fujita, Shmaryu M. Shvartsman, Michael R. Thompson, Michael A. Morich, Labros S. Petropoulos, and Vishnu C. Srivastava, "New applications of inverse methods in the design of MRI coils", Int. J. of Applied Electromagnetics and Mechanics, 9, 277-290, (1998). Crozier has introduced a stochastic optimization technique that was successfully used to design symmetric, compact MRI magnets. See S. Crozier and D. M. Doddrell, "Compact MRI magnet design by stochastic optimization," J. Magn. Reson.127, 233-237 (1997); and U.S. Pat. No. 5,818,319.
In general, the design of superconducting MRI magnets requires the consideration of various parameters. These include: central magnetic field strength, peak field in the superconductors, spatial homogeneity within the dsv, geometrical constraints, weight, and cost. The challenge in designing a compact magnet is the retention of high homogeneity conditions in the dsv, as magnet homogeneity is strongly dependent on the overall length of the coil structure. A measure of this fact is the relaxation factor .gamma.=d/R, (see FIG. 1a), where d is the distance from the end of the magnet to the beginning of the dsv on axis and R is the free bore radius. The smaller the value of .gamma., the more difficult it is to obtain a desired homogeneity level in the dsv.